Jeremy Corbyn has caved in to pressure and suspended Naz Shah, the Bradford West MP, over remarks she made about Israel on Facebook.

Shortly before he faced David Cameron in the House of Commons on Wednesday afternoon Corbyn had issued a statement saying that he had accepted Shah’s “fulsome” apology for a series of posts from 2014 in which she appeared to endorse a suggestion that Israelis be deported to the United States.

Even after the prime minister said it was “extraordinary,” that she continued to hold the Labour whip, and accused the Labour leader of failing to get to grips with antisemitisim in his party, Corbyn’s aides defended Shah, saying the comments were antisemitic but the MP had “shocked herself,” and did not mean what she said.

But later in the day, Labour announced that the Bradford West MP had been suspended, “by mutual agreement,” while claims against her were investigated by the compliance committee of Labour’s national executive committee.

The allegations centre around a 2014 Facebook post, in which Shah shared a graphic of Israel’s outline superimposed on a map of the US under the headline “Solution for Israel-Palestine Conflict – Relocate Israel into United States”, with the comment: “Problem solved.”

A Labour party spokesman said: “Jeremy Corbyn and Naz Shah have mutually agreed that she is administratively suspended from the Labour party by the general secretary. Pending investigation, she is unable to take part in any party activity and the whip is removed.”

Sources close to Corbyn denied that they had edited an article in Jewish News, in which Shah apologised. It was alleged in an article on BuzzFeed that the article had been changed, to remove references to the wider challenge of antisemitism on the left but senior party sources insisted that was “categorically not the case”, and the only changes had been stylistic. BuzzFeed later accepted that this was the case and that “nobody in Jeremy Corbyn’s office or Labour HQ saw or edited the draft referred to in our [BuzzFeed’s] original story”.

Later, Shah issued a statement, by email, saying: “The statement referred to by BuzzFeed was neither drafted by me nor approved by me. This was a very personal issue which I felt required a very personal response.

“I had caused the offence, it was right that I wrote my own apology. I sent my final statement to the Labour party for information. At no point was it changed by my party.”

Labour backbenchers were exasperated at the less than sure-footed handling of the crisis by the leadership; but there was considerable sympathy for the popular MP, who came from a tough family background to defeat George Galloway at last year’s general election in a sometimes bitter campaign. “In my book, she’s a heroine,” said one party source.

She told MPs: “I wholeheartedly apologise to this house for the words I used before I became a member. I accept and understand that the words I used caused upset and hurt to the Jewish community and I deeply regret that.”

But shadow energy secretary, Lisa Nandy, was among Labour figures saying the party faced “real problems” if it was seen not to apply the same standards to MPs as to other activists.

John Woodcock, MP and former chair of the Labour Friends of Israel, said: “The handling of this has been a mess. But the most important thing is that the Labour leadership properly acknowledges now the scale of the antisemitism problem that is growing in the party.”

“This is abhorrent to our values as a party. It ought to transcend views on the leadership and wider party direction but unless and until it is gripped by everyone from Jeremy downwards it is going to fester and undermine everything we do.”

Shah’s suspension was the latest in a series of incidents which have raised questions about antisemitism in the Labour party. Former parliamentary candidate Vicki Kirby was recently suspended, after being readmitted to the party following antisemitic Tweets, including comments about Jews having “big noses”.

The latest involved the suspension of Khadim Hussain, a Labourcouncillor and former lord mayor of Bradford, who was put underinvestigation for sharing a Facebook post that complained “your school education system only tells you about Anne Frank and the 6 million Zionists that were killed by Hitler”. He has now quit the party.

Jonathan Arkush, president of the Board of Deputies, an umbrella organisation representing British Jews, said earlier this month: “In the last few weeks we have witnessed a stream of clear cut cases of antisemitism in the Labour party, which can’t just be fobbed off as differences over Israel.”